Did Thomas Piketty Get His Math Wrong?

One of the most common approaches for people writing about Thomas Piketty’s blockbuster book “Capital in the 21st Century,” about global inequality, has been to critique his theories and predictions while effusively praising his data collection. Mr. Piketty, after all, did yeoman’s work compiling data from tax and other records to try to determine a history of wealth inequality around the world.

But now The Financial Times is throwing doubt on the data at the core of Mr. Piketty’s work, in a blockbuster report that will open a new debate on how reliable the book’s excavation of historical patterns of income and wealth truly are. At issue: Is the most influential economics book of the year built on bad math?

“The central theme of Prof Piketty’s work is that wealth inequalities are heading back up to levels last seen before the first world war,” writes Chris Giles, the economics editor of The Financial Times. “The investigation undercuts this claim, indicating there is little evidence in Prof Piketty’s original sources to bear out the thesis that an increasing share of total wealth is held by the richest few.”

Here is a detailed walk-through of the problems Mr. Giles alleges, and Mr. Piketty’s detailed response. We have contacted Mr. Piketty, a French economist, and his publisher, Harvard University Press, for further comment. May 24 update: In an e-mail to me Saturday morning, Mr. Piketty wrote: “Of course I welcome open debate and new series. This is why I put everything online.”

The Financial Times draws comparisons with the spreadsheet and other errors discovered last year that undermined work by Carmen Reinhart and Kenneth Rogoff on the relationship between government debt and growth. But what problems did The Financial Times discover and how much do they potentially undermine Mr. Piketty’s book?

Some of the issues identified by Mr. Giles appear to be clear-cut errors, and others are more in the realm of judgment calls in analyzing data that may not be fully explained by Mr. Piketty but are not necessarily wrong. Here are some of the specific potential problems that The Financial Times identifies and how they may come to bear on how we think about wealth, inequality and Mr. Piketty’s exploration of it.

Simple data errors. In the Reinhart-Rogoff case, a simple math error in an Excel spreadsheet had a relatively small impact on their final result, but it generated an outsize share of the attention to a broader critique of their data.

Mr. Giles identifies a couple of places where Mr. Piketty’s spreadsheets include what appear to be incorrect numbers, pulling a number for share of wealth held by the top 1 percent in Sweden from 1908 instead of the 1920 level that was intended. These errors may be embarrassing — and easy to understand — but can also be inevitable when pulling thousands of data points together as part of a large study. It is not clear that they have a major impact on Mr. Piketty’s conclusion, though it would be unsurprising, based on the Reinhart-Rogoff experience, if they get significant attention.

Arbitrary or unexplained changes. Mr. Giles examined many of the formulas in Mr. Piketty’s spreadsheets and found unexplained modifications to some of the data points, for example adding two percentage points to the share of wealth held by the top 1 percent in the United States in 1970, and calculating the share of British wealth held by the top 10 percent in 1870 by adding seemingly arbitrary numbers to the share held by the top 1 percent.

Image

The economist Thomas Piketty said he welcomed scrutiny of his data. That's why he put it all online, he said.CreditJustin Sullivan/Getty Images

Questionable methods to arrive at conclusions. Mr. Giles notes that Mr. Piketty arrives at estimates of European wealth inequality by averaging results for three countries where he has data, Britain, France, and Sweden, arguing that this is a poor way to weight because of Sweden’s much smaller population.

More significantly, Mr. Giles argues that Mr. Piketty constructed data where there is no cited source. For example, in data for the top 10 percent wealth share in the United States before 1950, “none of the sources Prof. Piketty uses contain these numbers, hence he assumes the top 10 percent wealth share is his estimate for the top 1 percent share plus 36 percentage points,” he wrote. “However, there is no explanation for this number, nor why it should stay constant over time.”

Mr. Giles also argues that Mr. Piketty combines different data sources arbitrarily, using surveys of households in the United States versus estate tax data for Britain, for example.

But does it matter? Mr. Giles attempts to reconstruct estimates of wealth inequality, correcting for what he describes as Mr. Piketty’s errors. He finds significantly less evidence of a rising disparity.

Speaking of Britain, for example, Mr. Giles writes, “There seems to be little consistent evidence of any upward trend in wealth inequality of the top 1 percent.” He further writes that if one incorporates the different British data into numbers for Europe as a whole, and weights by population instead of weighting Britain, France and Sweden equally, “there is no sign that wealth inequality in Europe is rising again.”

That is a damning conclusion, and if it holds up to scrutiny, would significantly undermine the case Mr. Piketty mounts. But Mr. Giles himself writes that “while this post is clear about what is wrong with Piketty’s charts, it is much less certain about the truth.”

Mr. Piketty, in his response to The Financial Times and in his e-mail on to me, said that research using other methodologies has affirmed his broad findings, citing work by Emmanuel Saez and Gabriel Zucman published since his book was written.

“As I make clear in the book, in the online appendix, and in the many technical papers I have written on this topic, one needs to make a number of adjustments to the raw data sources so as to make them more homogeneous over time and across countries,” he told the F.T. He added, “I have tried in the context of this book to make the most justified choices and arbitrages about data sources and adjustments. I have no doubt that my historical data series can be improved and will be improved in the future (this is why I put everything online).”

He did not specifically address the accusations of data-entry errors or give detailed responses to some of Mr. Giles’s criticisms about questionable assumptions that underlie Mr. Piketty’s broader work.

But in his e-mail to me, he wrote with an almost jovial tone: “Every wealth ranking in the world shows that the top is rising faster than average wealth,” adding, “If the FT comes with a wealth ranking showing a different conclusion, they should publish it!”

It is always a difficult challenge trying to examine economic history given spotty data from the past and variations in how different countries collect and define data. The new Financial Times report will surely be examined by specialists and start an important debate over what we really know about wealth inequality — and whether the best-selling economics book of the year gets its figures right.

The Upshot: The Upshot presents news, analysis
and graphics about politics
and policy. Online, Justin Wolfers
offers a counterpoint to the critique
of Thomas Piketty’s book.

A version of this article appears in print on , on Page B1 of the New York edition with the headline: Economist’s Inequality Study Faces Questions. Order Reprints | Today’s Paper | Subscribe